Rigidity measurement apparatus and rigidity measurement method

ABSTRACT

A rigidity measurement apparatus is a rigidity measurement apparatus that measures rigidity of an object to be measured and includes a load estimator, a displacement calculator, and a rigidity calculator. The load estimator estimates a load applied to a measurement point set on the object to be measured by using a captured image of the object to be measured. The displacement calculator calculates a displacement of the measurement point by using the captured image. The rigidity calculator calculates the rigidity of the object to be measured by using the load and the displacement.

TECHNICAL FIELD

The present disclosure relates to a rigidity measurement apparatus and arigidity measurement method for measuring rigidity of an object to bemeasured.

BACKGROUND ART

Unexamined Japanese Patent Publication No. 2000-55776 discloses a methodfor measuring bending rigidity of a structure. According to this method,bending rigidity of an object to be measured can be obtained bydisposing a plurality of vibration sensors on the object to be measured,giving impact to the object to be measured, and then calculatingpropagation velocities of vibrations obtained by the vibration sensors.

SUMMARY OF THE INVENTION

The present disclosure provides a rigidity measurement apparatus thatmakes it possible to measure rigidity of an object to be measured easilyat low cost by using a captured image of the object to be measured.

A rigidity measurement apparatus according to the present disclosure isa rigidity measurement apparatus that measures rigidity of an object tobe measured and includes a load estimator, a displacement calculator,and a rigidity calculator. The load estimator estimates a load appliesto a measurement point set on an object to be measured by using acaptured image of the object to be measured. The displacement calculatorcalculates a displacement of the measurement point by using the capturedimage. The rigidity calculator calculates rigidity of the object to bemeasured by using the load and the displacement.

A rigidity measurement method according to the present disclosure is arigidity measurement method for measuring rigidity of an object to bemeasured and includes estimating a load, calculating a displacement, andcalculating rigidity. In the estimating the load, a load applied to ameasurement point set on an object to be measured is estimated by usinga captured image of the object to be measured. In the calculating thedisplacement, a displacement of the object to be measured is calculatedby using the captured image. In the calculating the rigidity, rigidityof the object to be measured is calculated by using the load and thedisplacement.

A rigidity measurement apparatus and a rigidity measurement methodaccording to the present disclosure make it possible to measure rigidityof an object to be measured easily at low cost by using a captured imageof the object to be measured.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an appearance view illustrating an example of a configurationof a rigidity measurement system according to a first exemplaryembodiment.

FIG. 2 is a block diagram illustrating an example of a configuration ofthe rigidity measurement apparatus according to the first exemplaryembodiment.

FIG. 3 is a block diagram illustrating another example of aconfiguration of the rigidity measurement apparatus according to thefirst exemplary embodiment.

FIG. 4 is a flowchart illustrating an operation of the rigiditymeasurement apparatus according to the first exemplary embodiment.

FIG. 5 is a flowchart illustrating another operation of the rigiditymeasurement apparatus according to the first exemplary embodiment.

FIG. 6A illustrates an example of a captured image of a bridge.

FIG. 6B illustrates another example of the captured image of the bridge.

FIG. 7 illustrates an example of a way in which measurement points seton a bridge are disposed.

FIG. 8 illustrates an example of displacements calculated by adisplacement calculator.

FIG. 9 illustrates a coordinate set on the bridge.

FIG. 10 illustrates an example of a displacement distribution and a loaddistribution of the bridge.

FIG. 11 illustrates another example of the displacement distribution andthe load distribution of the bridge.

FIG. 12 illustrates an example of the rigidity distribution of thebridge.

FIG. 13 illustrates an example of a positional relationship between abridge and imaging devices.

FIG. 14 illustrates a cross section of the bridge.

FIG. 15A illustrates another example of the captured image of a bridge.

FIG. 15B illustrates another example of the way in which measurementpoints set on the bridge are disposed.

FIG. 15C illustrates a cable length of the bridge.

FIG. 15D illustrates another state of the cable length of the bridge.

FIG. 16 is a block diagram illustrating an example of a configuration ofa rigidity measurement apparatus according to a second exemplaryembodiment.

FIG. 17 illustrates an example of a captured image of a bridge accordingto the second exemplary embodiment.

FIG. 18 is a block diagram illustrating another example of theconfiguration of the rigidity measurement apparatus according to thesecond exemplary embodiment.

FIG. 19A illustrates an example of visualization of a rigiditydistribution.

FIG. 19B illustrates an example of a result in a case where it isdetermined that there is abnormality.

FIG. 20 illustrates an example of a result of visualization of adisplacement distribution and a load distribution.

DESCRIPTION OF EMBODIMENTS

Hereinafter, exemplary embodiments will be described in detail withreference to the drawings as appropriate. However, detailed descriptionbeyond necessity may be omitted. For example, detailed description of amatter that has been already known well or repeated description ofsubstantially the same configuration may be omitted. Such omissions areaimed to prevent the following description from being redundant morethan necessary, and to help those skilled in the art easily understandthe following description.

It should be noted that the attached drawings and the followingdescription are provided for those skilled in the art to fullyunderstand the present disclosure, and are not intended to limit thesubject matter as described in the appended claims.

First Exemplary Embodiment

A first exemplary embodiment is described with reference to FIGS. 1through 15D.

1-1. Configuration 1-1-1. Capturing of Object to be Measured

FIG. 1 is an appearance view illustrating an example of a configurationof rigidity measurement system 1 according to the first exemplaryembodiment. Rigidity measurement system 1 includes camera 101 andrigidity measurement apparatus 200. Camera 101 captures bridge 102plural times within a predetermined period and thus generates aplurality of captured images of bridge 102. Camera 101 captures bridge102 plural times, for example, at predetermined time intervals.

The plurality of captured images generated by camera 101 are supplied torigidity measurement apparatus 200. Rigidity measurement apparatus 200calculates a rigidity distribution indicative of a spatial distributionof rigidity of whole bridge 102 from the plurality of captured imagesinput. In the present exemplary embodiment, a case where camera 101 isused as an imaging device and bridge 102 is used as an object to bemeasured is described as an example.

1-1-2. Configuration of Rigidity Measurement Apparatus

FIG. 2 is a block diagram illustrating an example of a configuration ofrigidity measurement apparatus 200 according to the first exemplaryembodiment. As illustrated in FIG. 2, rigidity measurement apparatus 200includes input output I/F 210, controller 220, displacement calculator230, load estimator 240, rigidity calculator 250, and memory 260.Rigidity measurement apparatus 200 has, for example, a non-volatilememory in which a program is stored, a volatile memory that is atemporary storage region for execution of the program, an input outputport, and a processor that executes the program.

Input output I/F 210 receives input of the plurality of captured imagesof bridge 102 captured within a predetermined period. Input output I/F210 outputs a rigidity distribution (rigidity values at a plurality ofmeasurement points and a state of distribution of the rigidity values)of bridge 102 calculated by rigidity calculator 250. Input output I/F210 receives input of the plurality of captured images generated bycamera 101, for example, wirelessly, through a wire, or through arecording medium. Then, input output I/F 210 stores the plurality ofcaptured images in memory 260. Furthermore, input output I/F 210supplies the rigidity distribution of bridge 102 calculated by rigiditycalculator 250, for example, to a display (not illustrated), forexample, wirelessly, through a wire, or through the recording medium.The display displays the rigidity distribution supplied from rigiditymeasurement apparatus 200.

Controller 220 controls an operation of each unit of rigiditymeasurement apparatus 200.

Displacement calculator 230 calculates a displacement of a measurementpoint set on an object to be measured by using a captured image of theobject to be measured. More specifically, displacement calculator 230detects bridge 102 in each of the plurality of captured images generatedby camera 101, which are stored in memory 260. Then, displacementcalculator 230 calculates spatial displacements at a plurality ofmeasurement points set on bridge 102. Displacement calculator 230 thuscalculates a displacement distribution (displacement amounts of theplurality of measurement points and a state of distribution of thedisplacement amounts) of bridge 102. Then, displacement calculator 230stores the displacement distribution in memory 260.

Load estimator 240 estimates a load applied to a measurement point seton an object to be measured by using a captured image of the object tobe measured. More specifically, load estimator 240 detects a load sourceon bridge 102 in each of a plurality of captured images stored in memory260. After detecting the load source such as a vehicle that applies aload on bridge 102, load estimator 240 detects a kind of load source anda position of the load source on bridge 102. Then, load estimator 240acquires a load value corresponding to the kind of load source that isstored in advance in memory 260. Alternatively, a load source thatapplies a load on bridge 102 may be determined in advance, and loadestimator 240 may acquire a predetermined load value that is stored inadvance in memory 260. Specifically, in a case where a load source isfixed to a crane truck, load estimator 240 may acquire a load value of acrane truck stored in memory 260. In this case, each unit of rigiditymeasurement apparatus 200 performs processing by using only a capturedimage including a crane truck. Load estimator 240 calculates a loaddistribution indicative of a spatial distribution of a load applied tobridge 102 by using the position of the load source and the acquiredload value.

In a case where a measurement point and the position of the load sourcematch, load estimator 240 may use a load value stored in memory 260 as aload applied to the measurement point when estimating the load appliedto the measurement point. In a case where a measurement point and theposition of the load source do not match, load estimator 240 mayestimate a load applied to the measurement point in accordance with adistance between the measurement point and the position of the loadsource and the load value stored in memory 260.

Rigidity calculator 250 calculates a rigidity distribution indicative ofa spatial distribution of rigidity on an object to be measured by usinga displacement distribution and a load distribution. Specifically,rigidity calculator 250 calculates a rigidity distribution of bridge 102by using a displacement distribution calculated by displacementcalculator 230 and a load distribution calculated by load estimator 240.Then, rigidity calculator 250 stores the rigidity distribution in memory260.

Memory 260 stores captured images supplied from input output I/F 210.Furthermore, memory 260 is used as a work memory for each unit. Forexample, memory 260 stores a displacement and a displacementdistribution calculated by displacement calculator 230. Memory 260stores a load distribution calculated by load estimator 240 or loadvalues for respective kinds of load sources such as a vehicle. Memory260 stores a rigidity distribution of bridge 102 calculated by rigiditycalculator 250. Memory 260 is configured, for example, with asemiconductor storage element that is capable of operating at a highspeed such as a dynamic random access memory (DRAM).

All or part of functions of rigidity measurement apparatus 200 isachieved, for example, by execution of a program stored in thenon-volatile memory by the processor.

1-1-3. Another Configuration of Rigidity Measurement Apparatus

Bridge 102 is not always located at a same position in a plurality ofcaptured images generated by camera 101. In such a case, an error occursin a displacement calculated by displacement calculator 230. Therigidity measurement apparatus may have a function of correcting thedisplacement calculated by displacement calculator 230 in order to dealwith this error.

FIG. 3 is a block diagram illustrating another configuration of therigidity measurement apparatus according to the first exemplaryembodiment. In rigidity measurement apparatus 201 of FIG. 3, constituentelements that perform identical operations to those of rigiditymeasurement apparatus 200 of FIG. 2 are given identical reference signsand are not described repeatedly.

Controller 221 controls an operation of each unit of rigiditymeasurement apparatus 201.

Rigidity measurement apparatus 201 includes corrector 270. Corrector 270corrects displacements of a plurality of measurement points calculatedby displacement calculator 230 by using a displacement (referencedisplacement) of a predetermined reference measurement point calculatedby displacement calculator 230. More specifically, corrector 270corrects displacements of measurement points other than thepredetermined reference measurement point set on bridge 102 in acaptured image by using a reference displacement of the predeterminedreference measurement point as a reference. Corrector 270 thus correctsa displacement distribution. Then, corrector 270 stores the correcteddisplacement distribution in memory 260. The reference measurement pointis, for example, a point that is assumed to be displaced by a smallestamount among the plurality of measurement points.

Rigidity calculator 251 calculates a rigidity distribution from adisplacement distribution corrected by corrector 270 and a loaddistribution calculated by load estimator 240. Then, rigidity calculator251 stores the rigidity distribution in memory 260.

1-2. Operation 1-2-1. Operation without Correction

FIG. 4 is a flowchart illustrating an operation of rigidity measurementapparatus 200 according to the first exemplary embodiment.

(Captured Image Acquisition Step S310)

Controller 220 acquires captured images via input output I/F 210. Thecaptured images are images of bridge 102 captured within a predeterminedperiod by camera 101. Controller 220 stores the acquired captured imagesin memory 260.

(Displacement Calculation Step S320)

Controller 220 causes displacement calculator 230 to calculate atemporal displacement at a plurality of measurement points set on bridge102. In particular, in a case where bending rigidity that will bedescribed later is calculated, displacement calculator 230 calculatesdisplacements of three or more measurement points. Displacementcalculator 230 takes out the plurality of captured images stored inmemory 260 in order of photographing time and calculates a displacementof bridge 102 for each of the captured images. Displacement calculator230 calculates a displacement distribution from the calculateddisplacement. Then, displacement calculator 230 stores the displacementdistribution in memory 260.

(Load Estimation Step S340)

Controller 220 causes load estimator 240 to calculate a loaddistribution of bridge 102. Load estimator 240 recognizes a kind and aposition of a load source (e.g., a vehicle) from the captured imagesstored in memory 260 by image recognition. For example, in a case wherethe load source is a vehicle, load estimator 240 recognizes a kind ofvehicle and a running position of the vehicle on bridge 102. Loadestimator 240 acquires a load value corresponding to the recognized kindof load source among load values for respective kinds that are stored inadvance in memory 260. Load estimator 240 calculates a spatial loaddistribution by using the load value and the position of the loadsource. Then, load estimator 240 stores the load distribution in memory260. Load estimator 240 may acquire a load value not from memory 260 butfrom an external database via I/F 210. In a case where a kind of loadsource is determined in advance, load estimator 240 may detect only aposition of the load source and use a predetermined load value stored inmemory 260 in advance as a corresponding load value.

(Rigidity calculation step S350)

Controller 220 causes rigidity calculator 250 to calculate a rigiditydistribution of whole bridge 102 by using the displacement distributioncalculated by displacement calculator 230 and the load distributioncalculated by load estimator 240. Rigidity calculator 250 reads out thedisplacement distribution and the load distribution stored in memory 260and calculates the rigidity distribution of whole bridge 102. Then,rigidity calculator 250 stores the rigidity distribution in memory 260.Controller 220 outputs the rigidity distribution of whole bridge 102stored in memory 260 via input output I/F 210.

Although the steps are described in order of displacement calculationstep S320 and then load estimation step S340 in FIG. 4, the steps may beperformed in order of load estimation step S340 and then displacementcalculation step S320. In this case, displacement calculation step S320can be suspended while no load source is present.

1-2-2. Operation with Correction

FIG. 5 is a flowchart illustrating another operation of the rigiditymeasurement apparatus according to the first exemplary embodiment. FIG.5 illustrates an operation of rigidity measurement apparatus 201.

In FIG. 5, steps in which identical operations to those in the flowchartof FIG. 4 are performed are given identical reference signs and are notdescribed repeatedly.

(Displacement Correction Step S330)

Controller 221 causes corrector 270 to correct displacements at aplurality of measurement points calculated by displacement calculator230. Corrector 270 reads out temporal displacements at the plurality ofmeasurement points stored in memory 260 and corrects each displacementby using a reference displacement. Corrector 270 stores the correcteddisplacements in memory 260.

(Rigidity Calculation Step S351)

Controller 221 causes rigidity calculator 251 to calculate a rigiditydistribution by using a displacement distribution at the plurality ofmeasurement points corrected by corrector 270 and a load distributioncalculated by load estimator 240. Rigidity calculator 251 reads out thedisplacement distribution and the load distribution at the plurality ofmeasurement points stored in memory 260 and calculates the rigiditydistribution. Rigidity calculator 251 stores the calculated rigiditydistribution in memory 260.

The processes in displacement correction step S330 and rigiditycalculation step S351 may be different procedures that aremathematically equivalent or may be collectively performed as a unifiedprocedure as a result.

1-2-3. Operation Example 1

An example of an operation of rigidity measurement apparatus 201 isdescribed herein.

Controller 221 acquires a plurality of captured images of bridge 102 viainput output I/F 210 as illustrated in FIG. 1. Controller 221 stores theplurality of captured images in memory 260.

FIG. 6A illustrates an example of a captured image of bridge 102. FIG.6B illustrates another example of the captured image of bridge 102.Captured image 400 illustrated in FIG. 6A and captured image 401illustrated in FIG. 6B are images of bridge 102 that are captured atdifferent times. Captured images 400 and 401 show that vehicle 402 thatis a load source is present on bridge 102. In captured image 400,vehicle 402 is present on bridge support 103 for bridge 102, and bridge102 is not displaced. Meanwhile, in captured image 401, vehicle 402 islocated close to a center of bridge 102, and bridge 102 is displaced. Asdescribed above, an object (e.g., vehicle 402) different from bridge 102may be included in a captured image.

Displacement calculator 230 detects bridge 102 present in the capturedimage by using an existing image recognition technology. Displacementcalculator 230 detects coordinates of a plurality of measurement pointsset on detected bridge 102.

FIG. 7 illustrates an example of a way in which the plurality ofmeasurement points set on bridge 102 are disposed.

In FIG. 7, measurement points 501 through 511 are the plurality ofmeasurement points set on bridge 102. The measurement points may be setin advance by a user or may be set after bridge 102 is automaticallydetected by image recognition. In FIG. 7, the measurement points are setat almost regular intervals, but the effects of the present exemplaryembodiment can be obtained even in a case where the measurement pointsare set at irregular intervals. In the present exemplary embodiment, atleast one of the plurality of measurement points is set as a referencemeasurement point. It is assumed here that the reference measurementpoint is a measurement point that is affected by a load or the likeleast and is less displaced than other measurement points. In the firstexemplary embodiment, measurement point 501 and measurement point 511are used as the reference measurement points. Measurement point 501 andmeasurement point 511 are set close to points of contact between bridgesupports 103 of bridge 102 and substructures (not illustrated) placed inground that support bridge supports 103.

Displacement calculator 230 takes out the plurality of captured imagesstored in memory 260 in order of photographing time and calculates adisplacement of bridge 102 for each of the captured images. Displacementcalculator 230 calculates a displacement at each measurement point, forexample, between image 400 and image 401. Displacement calculator 230can use block matching or a correlation method as a method forcalculating a displacement in captured images. Examples of thecorrelation method include a normalized cross correlation method, aphase correlation method, and a laser speckle correlation method.Furthermore, displacement calculator 230 may use a general displacementcalculation method such as a sampling moire method or a feature pointtracking method. Accuracy of displacement calculation may be pixel-orderaccuracy or may be subpixel-order accuracy.

FIG. 8 illustrates an example of displacements calculated bydisplacement calculator 230. FIG. 8 illustrates position coordinates (x,y) of measurement points 501 through 511 in a plurality of capturedimages (Frame 1, Frame 2, Frame 3, . . . , Frame n) of bridge 102captured within a predetermined period.

Position coordinates (x, y) of i-th measurement point Pi in capturedimage Frame t of bridge 102 captured at time t are expressed as Pi(x, y,t). A displacement of i-th measurement point Pi in Frame t is expressedas Di(x, y, t). Displacement Di(x, y, t) is a difference in positioncoordinates Pi of the measurement point between captured images. In thepresent exemplary embodiment, i is an integer in a range from 1 to 11.Measurement points P1 through P11 correspond to measurement points 501through 511.

For example, displacement Di(x, y, t) can be calculated by formula 1 byusing position coordinates Pi in a plurality of captured images that aretemporally adjacent.

Di(x,y,t)=Pi(x,y,t)−Pi(x,y,t−1)  [Formula 1]

Alternatively, displacement Di(x, y, t) may be calculated by formula 2by using position coordinates Pi in a reference captured image and eachcaptured image. The reference captured image is, for example, a capturedimage that is top in chronological order or an image of an object to bemeasured that can be regarded as being in a steady state.

Di(x,y,t)=Pi(x,y,t)−Pi(x,y,0)  [Formula 2]

In formula 2, Pi(x, y, 0) are position coordinates in the referencecaptured image.

Controller 221 corrects image distortion of an imaging optical system ofcamera 101 as needed. Controller 221 (an example of a scaling unit) mayperform scale correction of a displacement calculated by displacementcalculator 230 based on a distance between a measurement point andcamera 101 that captures bridge 102. The scale correction is correctionfor making a ratio of a displacement on a captured image to adisplacement in an actual space at one measurement point equal to aratio of a displacement on a captured image to a displacement in anactual space at another measurement point. Such correction may beperformed on a captured image or may be performed on a calculateddisplacement. Controller 221 may perform the scale correction, forexample, by using coordinates, in an actual space, of the measurementpoints stored in memory 260.

Corrector 270 reads out displacement Di(x, y, t) of each of themeasurement points stored in memory 260. Corrector 270 corrects eachdisplacement Di by using displacement D1(x, y, t) of predeterminedreference measurement point P1 (measurement point 501) among theplurality of measurement points. That is, corrector 270 subtracts, foreach captured image, displacement D1(x, y, t) of the referencemeasurement point from displacement Di(x, y, t) of each of themeasurement points. This makes it possible to eliminate influence of animage displacement that occurs in a case where x and y directions ofcamera 101 change during shooting.

Furthermore, corrector 270 may set reference measurement point P11(measurement point 511) different from reference measurement point P1and perform rotational transform of x and y coordinate values ofdisplacement Di(x, y, t) of each measurement point about the position ofreference measurement point P1 such that the value of displacementD11(x, y, t) of reference measurement point P11 becomes close to 0. Thismakes it possible to eliminate influence of a displacement of eachcaptured image that occurs in a case where a roll direction of camera101 changes during shooting. Corrector 270 stores the correcteddisplacements at the measurement points in memory 260.

The reference measurement point may be set on bridge 102 or may be seton an object other than bridge 102. For example, the referencemeasurement point may be set on a still object (e.g., a building) inbackground of a captured image. The number of reference measurementpoints may be increased, and amounts of parallel movement correction androtation correction in x and y directions of each calculation positionmay be optimized such that a sum of displacements of the referencemeasurement points becomes minimum. This makes it possible to reduceinfluence on displacement calculation caused by rotation or a change ofdirections of camera 101 during shooting. Alternatively, dominant motion(global motion) of a whole image may be detected by analyzing motion offrame images at a plurality of times, and a point in the image thatfollows this motion may be used as a reference measurement point.

In a case where it is anticipated that a displacement in a capturedimage caused, for example, by a direction or rotation of camera 101 iswithin an allowable range, correction of the displacement by corrector270 may be omitted.

FIG. 9 illustrates a coordinate set on bridge 102. FIG. 9 illustrates arelationship between displacement distribution y(x) and position x usedin the following description. As illustrated in FIG. 8, the followingdescription focuses especially on a displacement distribution in a ydirection of a bridge beam part among displacements obtained from therespective measurement points of bridge 102.

Load estimator 240 recognizes a kind (a vehicle type in a case of avehicle) and a position of a load source (e.g., a vehicle) by usingcaptured images stored in memory 260 by image recognition. Loadestimator 240 calculates a spatial load distribution by referring to thevehicle type recognition result and load values for respective vehicletypes stored in advance in memory 260. Then, load estimator 240 storesthe load distribution in memory 260. Load estimator 240 may recognize avehicle type or a specific vehicle by using machine learning.Furthermore, load estimator 240 recognizes a position of a vehicle in acaptured image. As the machine learning, template learning, vectorquantization, decision tree, neural network, Bayesian learning, or thelike can be used. In a case where a vehicle type is determined inadvance, it is only necessary to recognize only a position of a vehicle.Load estimator 240 may use, for image recognition, an identifier thathas directly learned a relationship between a vehicle image and avehicle weight.

Load estimator 240 may acquire a load distribution obtained, forexample, from another sensor placed on an object to be measured viainput output I/F 210.

FIG. 10 illustrates an example of a displacement distribution and a loaddistribution of the bridge. In FIG. 10, image 10 c is a captured image,and displacement distribution 10 a and load distribution 10 b are adisplacement distribution and a load distribution obtained for capturedimage 10 c, respectively. In captured image 10 c, vehicle 402 is locatedclose to a center of bridge 102, and bridge 102 is displaced. In thiscase, displacement distribution 10 a shows that a portion where vehicle402 is located is displaced most. Furthermore, load distribution 10 bshows that a load is applied to the portion where vehicle 402 islocated.

Similarly, FIG. 11 illustrates another example of the displacementdistribution and the load distribution of the bridge. FIG. 11illustrates displacement distribution 11 a and load distribution libobtained from captured image 11 c. Captured image 10 c and capturedimage 11 c are images of bridge 102 captured at different times. Incaptured image 11 c, vehicle 402 is located on left of a center ofbridge 102, and bridge 102 is displaced. Also in this case, displacementdistribution 11 a shows that a portion where vehicle 402 is located isdisplaced most. Furthermore, load distribution lib shows that a load isapplied to the portion where vehicle 402 is located.

Rigidity calculator 251 calculates a rigidity distribution by using thedisplacement distribution and the load distribution calculated by loadestimator 240. Rigidity calculator 251 calculates bending rigiditydistribution Sb(x), for example, by using a mechanics equation such asformula 3.

$\begin{matrix}{\frac{d^{4}{y(x)}}{{dx}^{4}} = \frac{w(x)}{{Sb}(x)}} & \left\lbrack {{Formula}\mspace{14mu} 3} \right\rbrack\end{matrix}$

In formula 3, x is a lateral position of bridge 102, y(x) is adisplacement distribution, and w(x) is a load distribution. Such adifferential equation can be numerically solved as described, forexample, in Hiroyuki KISU, et al, “A study for identification of bendingrigidity of a beam”, Transactions of the Japan Society of MechanicalEngineers, Series A, Vol. 70, No. 698, 2004.

In a case where an ill-posed problem occurs due to an insufficientcondition such as an insufficient number of measurement points or in acase where a measurement value contains noise, rigidity calculator 251may calculate rigidity by combining a constraint condition such asformula 4 or formula 5 with formula 3. Formula 4 shows that rigiditydoes not depend on position x, and formula 5 shows that rigidity changessmoothly spatially.

$\begin{matrix}{\frac{{dSb}(x)}{dx} = 0} & \left\lbrack {{Formula}\mspace{14mu} 4} \right\rbrack \\{\frac{d^{2}{{Sb}(x)}}{{dx}^{2}} = 0} & \left\lbrack {{Formula}\mspace{14mu} 5} \right\rbrack\end{matrix}$

FIG. 12 illustrates an example of the rigidity distribution of thebridge. FIG. 12 illustrates rigidity distribution 12 a that is constantthroughout a whole beam of bridge 102.

Rigidity calculator 251 may use another calculation method of settingevaluation function E(Sb) concerning Sb(x) such as formula 6 as anoptimization problem and calculating Sb(x) such that evaluation functionE(Sb) is minimized. In formula 6, |C|^(p) represents p-norm of functionC. Furthermore, λ₁ and λ₂ are determined in advance as weightparameters.

$\begin{matrix}{{E({Sb})} = {{{\frac{d^{4}{y(x)}}{{dx}^{4}} - \frac{w(x)}{{Sb}(x)}}}^{2} + {\lambda_{1}{\frac{{dSb}(x)}{dx}}^{1}} + {\lambda_{2}{\frac{d^{2}{{Sb}(x)}}{{dx}^{2}}}^{1}}}} & \left\lbrack {{Formula}\mspace{14mu} 6} \right\rbrack\end{matrix}$

In order to obtain a stable solution in a case where an ill-posedproblem occurs due to an insufficient condition such as an insufficientnumber of measurement points or in a case where a measurement valuecontains noise, rigidity calculator 251 may calculate a rigiditydistribution by combining displacement distributions and loaddistributions obtained from a plurality of captured images of samebridge 102 that have different load distributions. For example, rigiditycalculator 251 may calculate the rigidity distribution as illustrated inFIG. 12 by combining a plurality of pairs of the displacementdistributions and the load distributions at different times asillustrated in FIGS. 10 and 11. In this case, rigidity calculator 251calculates a common rigidity distribution by utilizing that bridge 102is same in different captured images. The plurality of captured imageshaving different load distributions can be easily obtained by taking amoving image of bridge 102 while vehicle 402 passes bridge 102. Thismakes it possible to more accurately obtain a rigidity distribution ofbridge 102.

1-2-4. Operation Example 2

Next, an example of calculation of shear rigidity Ss(x) is described. Inthis case, rigidity calculator 251 can calculate a shear rigiditydistribution by using a mechanics equation such as formula 7 as in thecase of bending rigidity. In formula 7, Sb is bending rigidity.

$\begin{matrix}{\frac{d^{4}{y(x)}}{{dx}^{4}} = {\frac{w(x)}{Sb} - {\frac{1}{{SS}(x)}\frac{d^{2}{w(x)}}{{dx}^{2}}}}} & \left\lbrack {{Formula}\mspace{14mu} 7} \right\rbrack\end{matrix}$

1-2-5. Operation Example 3

Next, an example of calculation of torsional rigidity St is describedwith reference to FIGS. 13 and 14. FIG. 13 illustrates an example of apositional relationship between a bridge and imaging devices. FIG. 14illustrates a cross section of the bridge. FIG. 14 illustrates a crosssection of bridge 102 taken along line A-A in FIG. 13.

In FIG. 13, an upper side is a far side of bridge 102, and a lower sideis a near side of bridge 102. It is assumed that vehicle 402 is runningfrom the near side to the far side. Camera 130 captures bridge 102 froma right side in a traveling direction of the vehicle. Camera 131captures bridge 102 from a left side in the traveling direction of thevehicle. That is, camera 130 (an example of one of a plurality ofimaging devices) is disposed on a side opposite to camera 131 (anexample of another one of the plurality of imaging devices) acrossbridge 102.

FIG. 14 illustrates a state where bridge 102 is twisted. Morespecifically, bridge 102 is twisted by a torsional angle ϕ due totorsional moment M_(T) caused by a load of vehicle 402. In FIG. 14,displacement Y_(L) and displacement Y_(R) are displacements that occurat a left end and a right end of bridge 102 due to the load of vehicle402, respectively. Displacement calculator 230 calculates displacementY_(R) and displacement Y_(L) from images captured by camera 130 andcamera 131, respectively.

Rigidity calculator 251 can calculate torsional rigidity St by usingformula 8.

$\begin{matrix}{{St} = \frac{M_{T}}{\phi}} & \left\lbrack {{Formula}\mspace{14mu} 8} \right\rbrack\end{matrix}$

Input I/F 210 receives input of two captured images of bridge 102 thatare captured in synchronization by camera 130 and camera 131. Camera 130and camera 131 are disposed on both sides of bridge 102 along adirection (a direction parallel with line A-A) orthogonal to a bridgeaxis as illustrated in FIG. 13. Displacement calculator 230 calculatesdisplacement distribution y_(R)(x) from the captured image generated bycamera 130 and calculates displacement distribution y_(L)(x) from thecaptured image generated by camera 131. Displacement calculator 230calculates torsional angle φ of bridge 102 by using y_(R)(x), y_(L)(x),and formula 9. In formula 9, Wb is a width of bridge 102, which isknown.

$\begin{matrix}{{\phi (x)} = {\arctan \mspace{11mu} \left( \frac{{y_{R}(x)} - {y_{L}(x)}}{W_{b}} \right)}} & \left\lbrack {{Formula}\mspace{14mu} 9} \right\rbrack\end{matrix}$

Furthermore, load estimator 240 finds position z of vehicle 402 in adirection orthogonal to the bridge axis by determining a lane on whichvehicle 402 is traveling based on the image showing traveling vehicle402. It is assumed that a position of the lane in a height direction isknown. In this case, load estimator 240 calculates torsional momentM_(T) by using load position z×load w×gravitational acceleration g.

1-2-6. Operation Example 4

Next, a case where axial rigidity Sa of a vertical cable of bridge 112having a suspension structure is described with reference to FIGS. 15Athrough 15D.

FIG. 15A illustrates another example of a captured image of a bridge. Asillustrated in FIG. 15A, bridge 112 has a suspension structure andincludes three vertical cables 151 through 153.

FIG. 15B illustrates another example of the way in which measurementpoints set on the bridge are disposed. As illustrated in FIG. 15B, bothend points of the vertical cables are set as measurement points 151 a,151 b, 152 a, 152 b, 153 a, and 153 b.

FIG. 15C illustrates a cable length of the bridge. FIG. 15C illustratesa case where no load is applied to bridge 112. FIG. 15C shows that thecable length of vertical cable 152 is L.

FIG. 15D illustrates another state of a cable length of the bridge. FIG.15D illustrates a state where a load is applied to bridge 112 by vehicle402 running on bridge 112. FIG. 15D shows that bridge 112 is warped dueto the load of vehicle 402 and a length of vertical cable 152 becomesL+δL.

In this case, rigidity calculator 251 can calculate axial rigidity Sa ofvertical cable 152 by formula 10. In formula 10, N is force applied tovertical cable 152 by the load and is calculated by load w of vehicle402×gravitational acceleration g. δL is an amount of elongation of acable length of vertical cable 152 that occurs due to load w. δL is adifference in displacement between measurement points 152 a and 152 b.δL can be calculated in a similar manner as for vertical cables 151 and153.

$\begin{matrix}{{Sa} = \frac{N}{\delta \; L}} & \left\lbrack {{Formula}\mspace{14mu} 10} \right\rbrack\end{matrix}$

A similar method can be applied not only in a case where a rigiditydistribution of a bridge support having a suspension structure iscalculated, but also in a case where a rigidity distribution of a wholecomplex structure such as a cable-stayed bridge, a harp bridge, anelectric wire having a cable structure, or a steel tower is calculated.

Although examples of calculation of bending rigidity, shear rigidity,torsional rigidity, and axial rigidity have been described in the firstexemplary embodiment, it is unnecessary to calculate all of these. It isunnecessary to calculate a rigidity parameter that can be ignored inadvance or an unnecessary rigidity parameter. Furthermore, a mechanicsequation used for calculation of rigidity may be simpler than the aboveformula or may be stricter than the above formula. Furthermore, amechanics equation including a plurality of kinds of rigidity parametersmay be used.

1-3. Effects and Other Benefits

As described above, rigidity measurement apparatus 200 according to thepresent exemplary embodiment is a rigidity measurement apparatus thatmeasures rigidity of an object to be measured and includes loadestimator 240, displacement calculator 230, and rigidity calculator 250.Load estimator 240 estimates a load applied to a measurement point seton bridge 102 by using a captured image of bridge 102. Displacementcalculator 230 calculates a displacement of a measurement point by usingthe captured images. Rigidity calculator 250 calculates rigidity ofbridge 102 by using the load and the displacement.

This makes it possible to remotely measure rigidity of an object to bemeasured.

Furthermore, load estimator 240 calculates a load distribution of bridge102 by estimating loads applied to a plurality of measurement points seton bridge 102. Displacement calculator 230 calculates a displacementdistribution of bridge 102 by calculating displacements of the pluralityof measurement points. Rigidity calculator 250 calculates a rigiditydistribution of bridge 102 by using the load distribution and thedisplacement distribution.

This makes it possible to remotely measure a rigidity distribution of awhole object to be measured.

It is therefore possible to acquire a displacement distribution and aload distribution of a whole structure of an object to be measured andthereby calculate a rigidity distribution of the whole structure of theobject to be measured easily at low cost. This makes it possible toeasily obtain strength evaluation of a structure. Furthermore, since animage is recorded, a state of appearance of an object to be measured canalso be grasped easily.

Furthermore, since camera 101 captures a wide range includingmeasurement points and a reference measurement point on an object to bemeasured, rigidity of the object to be measured can be measured withhigh accuracy while keeping influence of camera shake small.

Second Exemplary Embodiment

A second exemplary embodiment is described below with reference to FIGS.1 through 3, FIG. 7, and FIGS. 16 through 19B.

Bridge 102 is not always located at a same position in a plurality ofcaptured images generated by imaging device 101. In such a case, if acoordinate position of a measurement point set on one captured image isapplied to another captured image, there is a possibility that theapplied position of the measurement point be deviated from an originallyset position. Accordingly, displacement calculator 230 calculates adisplacement between deviated measurement points. In order to addressthis, rigidity measurement apparatus 202 according to the secondexemplary embodiment includes setting unit 280. Setting unit 280 sets aposition of a measurement point of an object to be measured in acaptured image for which a displacement is to be calculated by referringto a position of a measurement point on the object to be measured set inanother captured image.

2-1. Configuration

FIG. 16 is a block diagram illustrating an example of a configuration ofrigidity measurement apparatus 202 according to the second exemplaryembodiment. In FIG. 16, constituent elements that perform identicaloperations to FIG. 2 are given identical reference signs and are notdescribed repeatedly.

Rigidity measurement apparatus 202 according to the second exemplaryembodiment includes setting unit 280 that sets a measurement point inaddition to the configuration of rigidity measurement apparatus 200according to the first exemplary embodiment.

Setting unit 280 sets a measurement point based on an object to bemeasured. In other words, setting unit 280 sets a measurement point ofbridge 102 in a first captured image based on a measurement point set onbridge 102 in a second captured image. In the present exemplaryembodiment, it is assumed that an image-capturing position of imagingdevice 101 at a time of capturing of the first captured image and animage-capturing position of imaging device 101 at a time of capturing ofthe second captured image are different. Note that the present exemplaryembodiment is also applicable even in a case where the first capturedimage and the second captured image are captured in reverse order.

2-2. Operation

Rigidity measurement apparatus 200 according to the first exemplaryembodiment and rigidity measurement apparatus 202 according to thesecond exemplary embodiment are different only in terms of an operationfor setting a measurement point performed by setting unit 280, andtherefore only an operation of setting unit 280 is described.

In the second exemplary embodiment, the first captured image for which adisplacement is to be calculated is captured image 500 of FIG. 7.

FIG. 17 illustrates an example of the second captured image of bridge102 according to the second exemplary embodiment. FIG. 17 illustratescaptured image 800 and an example of a way in which measurement pointsset on bridge 102 in captured image 800 are disposed. Captured image 500and captured image 800 are images of bridge 102 captured from differentpositions.

In FIG. 17, measurement points 801 through 811 are measurement pointsset on bridge 102. Measurement points 801 through 811 may be set inadvance by a user or may be automatically set on bridge 102 after imagerecognition of bridge 102 as in the first exemplary embodiment.

It is assumed that a position of bridge 102 in captured image 800 isdeviated toward a lower right side relative to a position of bridge 102in captured image 500 as illustrated in FIGS. 7 and 17. In a case wherea position of a captured object to be measured is deviated between aplurality of captured images of the same object to be measured asdescribed above, there is a possibility that positions of measurementpoints set on bridge 102 be deviated (different) between the capturedimages.

In view of this, in the second exemplary embodiment, setting unit 280sets measurement points 501 through 511 (including a referencemeasurement point) on bridge 102 in captured image 500 of FIG. 7 basedon captured image 800 and positions of measurement points 801 through811 (including a reference measurement point).

Specifically, setting unit 280 determines the positions of themeasurement points in captured image 500 that correspond to themeasurement points of captured image 800 by using local features of animage, block matching, a correlation method, or the like. As the localfeatures, scale-invariant feature transform (SIFT), speeded up robustfeatures (SURF), or the like can be used.

Rigidity measurement apparatus 202 according to the second exemplaryembodiment may include corrector 270 (see rigidity measurement apparatus203 of FIG. 18) as in the first exemplary embodiment. FIG. 18 is a blockdiagram illustrating another example of a configuration of a rigiditymeasurement apparatus according to the second exemplary embodiment.

2-3. Effects and Other Benefits

As described above, rigidity measurement apparatus 202 according to thesecond exemplary embodiment further includes setting unit 280. Settingunit 280 sets a measurement point based on bridge 102.

This makes it possible to calculate a displacement at a same position onan object to be measured in a case where an object to be measured thatwas measured in past is measured again.

Accordingly, when a same object to be measured is captured again,measurement points in a captured image are set based on the object to bemeasured in a case where an image-capturing position or an imagingdevice changes. It is therefore possible to reduce trouble of setting alarge number of measurement points again. That is, it is possible toeasily make comparison between measurement results of the object to bemeasured captured at different times.

The present disclosure is also applicable, for example, even in a casewhere a posture of an imaging device changes when an object to bemeasured is captured plural times within a predetermined period.

Other Exemplary Embodiments

The first and second exemplary embodiments have been described above asan illustration of the technique disclosed in the present application.However, the technique of the present disclosure is not limited thereto,and can be also applied to exemplary embodiments in which changes,replacements, additions, omissions, and the like are made. Additionally,constituent elements described in the above exemplary embodiments can becombined to configure a new exemplary embodiment.

Hence, other exemplary embodiments are illustrated below.

Camera 101 may be provided separately from rigidity measurementapparatus 200 as illustrated in FIG. 1 or may be provided in rigiditymeasurement apparatus 200. A captured image may be a monochromatic imageor may be a color image (including a multi spectral image). Camera 101need not be a typical camera. Camera 101 may be a camera that detects anobject to be measured by using a distance measuring sensor or anacceleration sensor and output array data obtained by detection as animage.

In the above exemplary embodiments, a single camera is mainly used, buta plurality of cameras that capture different places of a same object tobe measured may be used as illustrated in FIG. 13. In this case, theprocesses to step S330 are performed for each of captured imagesgenerated by the plurality of cameras by using captured images capturedin synchronization by the plurality of cameras. In step S340 andsubsequent steps, similar processes can be performed by using alldisplacement distributions obtained from the plurality of capturedimages as a combination. This makes it possible to accurately measure adisplacement of an object to be measured that cannot be captured by asingle camera. That is, displacement calculator 230 may calculate adisplacement by using a plurality of captured images of object to bemeasured 102 captured in synchronization by the plurality of imagingdevices.

In the above exemplary embodiments, two-dimensional displacement Di(x,y) is calculated, but three-dimensional displacement Di(x, y, z) may becalculated by acquiring a depth image. A high-accuracy three-dimensionaldisplacement can be obtained by performing a similar procedure to theabove exemplary embodiments after displacement calculation. As a cameraor a method for generating the depth image, a stereo camera forsynchronized capturing using a plurality of cameras, a multi-view camerastereo method, a pattern projection method, a time-of-fight (TOF)camera, a laser displacement gauge, or the like can be used. That is,displacement calculator 230 may calculate a displacement by using adepth image including information indicative of a distance between ameasurement point and an imaging device that captures an object to bemeasured.

Although bridge 102 is illustrated as an example as an object to bemeasured in the above exemplary embodiments, similar effects can also beobtained even in a case where a construction such as a building, a steeltower, a chimney, a wall surface, a floor material, a plate material, asteel scaffolding, a road surface, a railway track, or a vehicle body isused as the object to be measured.

Furthermore, light captured by camera 101 may be ultraviolet ray, nearinfrared ray, or far infrared ray, as well as visible light.

Furthermore, a rigidity distribution calculated by rigidity calculator250 may be visualized. For example, controller 220 (an example of asuperimposed image generator) may generate a superimposed image bysuperimposing an image based on rigidity calculated by rigiditycalculator 250 on at least one of a plurality of captured images.Similarly, controller 220 may visualize displacement distribution 20 acalculated by displacement calculator 230 or load distribution 20 bcalculated by load estimator 240 by superimposing displacementdistribution 20 a or load distribution 20 b on captured image 20 c, asillustrated in FIG. 20. This allows a user to check an operation ofrigidity measurement apparatus 200. It is unnecessary to display all ofa displacement distribution, a load distribution, and a rigiditydistribution, and it is only necessary to display only a necessarydistribution.

Controller 220 generates a superimposed image by superimposing an imagebased on a rigidity distribution on a captured image of bridge 102, asillustrated in FIG. 19A. In FIG. 19A, broken line Q1 indicates arigidity distribution displayed in accordance with a position of bridge102. In FIG. 19A, a part of broken line Q1 depressed downward indicatesthat rigidity of part of bridge 102 has decreased. A rigiditydistribution may be expressed not only by using a graph, but also bygradation or colors. By displaying a rigidity distribution in this way,a spatial distribution of rigidity of bridge 102 can be easily grasped.In a case where a depth image is used, similar ways of display can beachieved by using 3D display.

Furthermore, rigidity calculator 250 may store a reference value ofrigidity of an object to be measured and determine whether or notcalculated rigidity is abnormal by using the reference value. Rigiditycalculator 250 determines that rigidity is abnormal, for example, in acase where the calculated rigidity is equal to or smaller than thereference value. Controller 220 may visualize not only a rigiditydistribution, but also a position of rigidity determined to be abnormalby rigidity calculator 250, as illustrated in FIG. 19B. In FIG. 19B, theposition of the abnormal rigidity is indicated by thick line Q2. Thatis, rigidity calculator 250 may output a result of determination as towhether or not rigidity is abnormal.

Furthermore, displacement calculator 230 may estimate a displacement ofa point other than a measurement point by spatially interpolatingcalculated displacements of a whole object to be measured. Furthermore,corrector 270 may correct a captured image or a displacement calculatedby displacement calculator 230 such that actual scales of an object tobe measured included in captured images become equal. In a case where acaptured image is corrected, corrector 270 performs correction beforedisplacement calculator 230 calculates a displacement.

Furthermore, rigidity calculator 250 may calculate a rigiditydistribution by combining a plurality of different load distributionsand displacement distributions corresponding to the load distributions.

It should be noted that, since the aforementioned exemplary embodimentsillustrate a technique of the present disclosure, various changes,replacements, additions, omissions, and the like can be made in theclaims and their equivalents.

INDUSTRIAL APPLICABILITY

A rigidity measurement apparatus according to the present disclosure isapplicable, for example, to gauging, measurement, analysis, diagnosis,and inspection of structural strength of a structure.

REFERENCE MARKS IN THE DRAWINGS

-   -   1: rigidity measurement system    -   101, 130, 131: camera (imaging device)    -   102, 112: bridge (object to be measured)    -   200, 201, 202, 203: rigidity measurement apparatus    -   210: input output I/F    -   220, 221: controller    -   230: displacement calculator    -   240: load estimator    -   250, 251: rigidity calculator    -   260: memory    -   270: corrector    -   280: setting unit

1. A rigidity measurement apparatus for measuring rigidity of a cableincluded in an object and suspending a structure of the object, therigidity measurement apparatus comprising: a displacement calculatorthat calculates a displacement of a length between two measurementpoints set on the cable by using a plurality of captured images in whichthe object was captured in a plurality of times; a load estimator thatestimates a load applied to the cable over time by using the pluralityof captured images; and a rigidity calculator that calculates therigidity of the cable by using the load and the displacement.
 2. Therigidity measurement apparatus according to claim 1, further comprisinga memory that stores a load value of a load source, wherein the loadestimator detects a position of the load source on the object by usingthe plurality of captured images and estimates the load applied to thecable by using the load value and the position of the load source. 3.The rigidity measurement apparatus according to claim 1, furthercomprising a memory that stores a load value corresponding to a kind ofa load source, wherein the load estimator detects a position and thekind of the load source on the object by using the plurality of capturedimages and estimates the load applied to the cable by using the loadvalue corresponding to the kind of the load source and the position ofthe load source.
 4. The rigidity measurement apparatus according toclaim 1, further comprising a memory configured to store a predeterminedload value, wherein the load estimator detects a position of a loadsource on the object by using the plurality of captured images andestimates the load applied to the cable by using the predetermined loadvalue and the position of the load source.
 5. The rigidity measurementapparatus according to claim 1, further comprising a setting unit thatsets the two measurement points based on the object.
 6. The rigiditymeasurement apparatus according to claim 1, further comprising acorrector, wherein the displacement calculator calculates a referencedisplacement of a predetermined reference measurement point, thecorrector corrects the displacement by using the reference displacement,and the rigidity calculator calculates the rigidity by using thecorrected displacement.
 7. The rigidity measurement apparatus accordingto claim 1, wherein the displacement calculator calculates thedisplacement by using block matching or a correlation method.
 8. Therigidity measurement apparatus according to claim 1, wherein the objectincludes a plurality of the cables, the load estimator calculates a loaddistribution of the object by estimating a load applied to each of theplurality of cables, the displacement calculator calculates adisplacement distribution of the object by calculating a displacement ofeach of the plurality of cables, and the rigidity calculator calculatesa rigidity distribution of the object by using the load distribution andthe displacement distribution.
 9. The rigidity measurement apparatusaccording to claim 8, wherein the rigidity calculator calculates therigidity distribution by combining a plurality of the load distributionsthat are different from one another and a plurality of the displacementdistributions corresponding to the plurality of the load distributions.10. The rigidity measurement apparatus according to claim 1, furthercomprising a superimposed image generator that generates a superimposedimage by superimposing an image based on the rigidity on the pluralityof captured images.
 11. The rigidity measurement apparatus according toclaim 1, wherein the rigidity calculator stores a reference value ofrigidity of the cable, determines whether or not the calculated rigidityis abnormal by using the reference value, and outputs a result of thedetermination.
 12. The rigidity measurement apparatus according to claim11, further comprising a superimposed image generator that generates asuperimposed image by superimposing an image based on the rigidity onthe plurality of captured images, wherein the superimposed imagegenerator visualizes the rigidity determined to be abnormal by therigidity calculator in the superimposed image.
 13. The rigiditymeasurement apparatus according to claim 1, further comprising a scalingunit that performs scale correction of the displacement based on adistance between the two measurement points and an imaging device thatcaptures the object.
 14. The rigidity measurement apparatus according toclaim 1, wherein the plurality of captured images are captured insynchronization by a plurality of imaging devices.
 15. The rigiditymeasurement apparatus according to claim 14, wherein one of theplurality of imaging devices is disposed on a side opposite to anotherone of the plurality of imaging devices across the object.
 16. Therigidity measurement apparatus according to claim 1, wherein theplurality of captured images include information indicative of adistance between the two measurement points and an imaging device thatcaptures the object, and the displacement calculator calculates thedisplacement by using the information of the plurality of capturedimages.
 17. The rigidity measurement apparatus according to claim 1,wherein the plurality of captured images include a reference capturedimage that is a top image in chronological order or an image in whichthe object is in a steady state.
 18. The rigidity measurement apparatusaccording to claim 1, wherein the object is a bridge having a suspensionstructure, a cable-stayed bridge, or a harp bridge.
 19. The rigiditymeasurement apparatus according to claim 1, wherein the cable is avertical cable.
 20. A rigidity measurement method of measuring rigidityof a cable included in an object and suspending a structure of theobject, the rigidity measurement method comprising: calculating adisplacement of a length between two measurement points set on the cableby using a plurality of captured images in which the object was capturedin a plurality of times; estimating a load applied to the cable overtime by using the plurality of captured images; and calculating therigidity of the cable by using the load and the displacement.